# gpais

Gaussian Process Adaptive Importance Sampling

**Topics**

uncertainty_quantification

**Specification**

*Alias:*gaussian_process_adaptive_importance_sampling*Arguments:*None

**Child Keywords:**

Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
---|---|---|---|

Optional |
Number of initial model evaluations used in build phase |
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Optional |
Seed of the random number generator |
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Optional |
Number of samples at which to evaluate an emulator (surrogate) |
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Optional |
File containing points you wish to use to build a surrogate |
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Optional |
Output file for surrogate model value evaluations |
||

Optional |
Number of iterations allowed for optimizers and adaptive UQ methods |
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Optional |
Values at which to estimate desired statistics for each response |
||

Optional |
Specify probability levels at which to estimate the corresponding response value |
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Optional |
Specify generalized relability levels at which to estimate the corresponding response value |
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Optional |
Selection of cumulative or complementary cumulative functions |
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Optional |
Selection of a random number generator |
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Optional |
Identifier for model block to be used by a method |

**Description**

`gpais`

is recommended for problems that have a relatively small
number of input variables (e.g. less than 10-20). This method, Gaussian
Process Adaptive Importance Sampling,
is outlined in the paper [DS14].

This method starts with an initial set of LHS samples and adds samples one at a time, with the goal of adaptively improving the estimate of the ideal importance density during the process. The approach uses a mixture of component densities. An iterative process is used to construct the sequence of improving component densities. At each iteration, a Gaussian process (GP) surrogate is used to help identify areas in the space where failure is likely to occur. The GPs are not used to directly calculate the failure probability; they are only used to approximate the importance density. Thus, the Gaussian process adaptive importance sampling algorithm overcomes limitations involving using a potentially inaccurate surrogate model directly in importance sampling calculations.